On two methods for approximating minimal surfaces in parametric form
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- by Takuya Tsuchiya PDF
- Math. Comp. 46 (1986), 517-529 Request permission
Abstract:
Two methods for approximating minimal surfaces in parametric form are considered. One minimizes the area of the surface, and the other the energy of the surface. The convergence of the algorithm of the first method is proved. The application of the second method to the approximation of conformal maps is examined. Several examples of computations are given.References
- R. Courant, Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, Interscience Publishers, Inc., New York, N.Y., 1950. Appendix by M. Schiffer. MR 0036317
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Masahiro Hinata, Masaaki Shimasaki, and Takeshi Kiyono, Numerical solution of Plateau’s problem by a finite element method, Math. Comp. 28 (1974), 45–60. MR 331819, DOI 10.1090/S0025-5718-1974-0331819-6
- H. Blaine Lawson Jr., Lectures on minimal submanifolds. Vol. I, Monografías de Matemática [Mathematical Monographs], vol. 14, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1977. MR 527121
- H. D. Mittelmann, On the approximation of capillary surfaces in a gravitational field, Computing 18 (1977), no. 2, 141–148 (English, with German summary). MR 436779, DOI 10.1007/BF02243623
- H. D. Mittelmann, On pointwise estimates for a finite element solution of nonlinear boundary value problems, SIAM J. Numer. Anal. 14 (1977), no. 4, 773–778. MR 445865, DOI 10.1137/0714053
- Hans-Detlef Mittelmann, On the approximate solution of nonlinear variational inequalities, Numer. Math. 29 (1977/78), no. 4, 451–462. MR 658146, DOI 10.1007/BF01432881
- Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. MR 0256278
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Math. Comp. 46 (1986), 517-529
- MSC: Primary 49D20; Secondary 49F10, 65E05
- DOI: https://doi.org/10.1090/S0025-5718-1986-0829622-1
- MathSciNet review: 829622